On 23 Sep 2013, at 12:41, Telmo Menezes wrote:
On Sat, Sep 21, 2013 at 9:43 PM, Bruno Marchal <marc...@ulb.ac.be>
On 21 Sep 2013, at 15:10, Telmo Menezes wrote:
On Fri, Sep 20, 2013 at 3:58 PM, Bruno Marchal <marc...@ulb.ac.be>
On 19 Sep 2013, at 16:51, Telmo Menezes wrote:
On Thu, Sep 19, 2013 at 4:31 PM, Bruno Marchal <marc...@ulb.ac.be>
If so, can't we say ~D~t and thus t?
Yes, t is a theorem, of G and most modal logic, but not of Z!
Isn't the only situation where ~Dt the one where this is no world?
~Dt, that is  f, inconsistency, is the type of the error, dream,
"near-death", or in-a-cul-de-sac.
Thus your interest in near-death experiences?
Yes. And in all "extreme" altered state of consciousness. Those
extreme cases provide key information.
We should *try* to avoid it, but we can't avoid it without loosing
The consistent machines face the dilemma between security and lack of
freedom-universality. With <>p = ~ ~p, here are equivalent way
<>t -> ~<>t
<>t -> <>  f
<>t ->  f
I don't understand how you arrive at this equivalence.
I use only the fact that (p -> q) is equivalent with (~q -> ~p) (the
contraposition rule, which is valid in classical propositional logic),
and the definition of <> p = ~ ~p. I use also that ~~p is equivalent
Note that p = ~~~~p = ~<> ~p. And,
~p = <> ~p
~<>p =  ~p
Like with the quantifier, a not (~) jumping above a modal sign makes
it into a diamond, if it was a bo, and a box, if it was a diamond.
Starting from <>t -> ~<>t. Contraposition gives ~~<>t -> ~<>t, and
this gives by above, <>t -> ~t, which gives
<>t -> f (as ~t = f, and ~f = t).
For the third one, starting from the first one again: <>t -> ~<>t,
By contraposition <>t -> ~<>t , but ~<>t = ~t =  f.
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